Chapter XI

The Two Aspects of Motion

To Aristotle space represented a relationship between objects, to Democritus it was a container in which the objects exist, to Einstein it was a medium connecting the objects. Modern science professes to follow Einstein, but in practice adopts a kind of hybrid viewpoint. Indeed, it is quite fashionable to contend that Einstein eliminated the need for a medium, even though it is clear that his “space” has all of the properties, aside from that of being a material substance, that are ever assigned to a hypothetical medium, and he unquestionably uses it as a medium in his theoretical structure. In fact, Einstein himself admits that his “space” is the equivalent of an “ether” and specifically uses the word “medium” to describe it.¹¹⁰

The findings of this work now assign a still different role to space. In the Reciprocal System, space is an aspect of motion. For the purpose of this description, however, we must visualize motion in a somewhat more general sense than that in which the term is customarily utilized. Ordinarily we conceive of motion as motion of something. However, the mathematical equations by means of which we describe the motion show no trace of this something, whatever it may be. The equation v = s/t, for instance, defines velocity, the quantitative measure of motion, in terms of space and time only, without bringing anything else into the picture. In this equation it is clear that motion is a relation between space and time—nothing more—and when this work describes space as an aspect of motion, this is the significance that is attached to the term “motion.“

The principal purpose of specifying that a particular motion is a motion of a particle or of something else is to identify the space-time and velocity with which we are dealing. In some instances it is possible to identify particular units of space and time independently of any moving object, and the relation of space to time under these conditions is also motion: a more generalized motion, we may say. Space is one aspect of motion, whether that motion is motion of something or not, and time is the other aspect.

When we are dealing with translatory motion, space manifests itself as extension. This is the familiar entity that we normally visualize whenever the term “space” is used. Hearing or seeing this word calls to mind a linear extension, an area, or a volume, depending on the context. For purposes of convenient reference we will hereafter apply the name “extension space” to this kind of space, irrespective of the dimensions involved. Extension space is the only kind of space that exists in the world of Aristotle, the world of Democritus, or the world of Einstein. When we characterize space as an aspect of motion, however, we introduce other kinds of space, since motion can be vibrational or rotational as well as translational, and one of the two reciprocal aspects of this vibrational or rotational motion is space, as herein defined, even though such space does not constitute extension in the normal sense of that term.

There is a somewhat general tendency to object to this new definition of “space” on the ground that it involves lumping together under one designation several entities of quite different character and is thus nothing but an artificial grouping without any physical justification. The truth, however, is just the opposite. This is the definition that conforms to the physical realities; that is, the physical principles applicable to space in general apply not only to extension space but also to the other kinds of space included within this definition. Hence this is the definition that must be used in order to arrive at the correct physical results.

As pointed out in the earlier discussion, the common practice of setting up definitions on a purely arbitrary basis or in conformity with prevailing viewpoints regarding the items to be defined, rather than making a serious effort to fit the definition to the physical situation, is a serious obstacle in the way of scientific progress. It is often stated that no definition can be wrong if it is logically formulated and consistently applied, and in a sense this is true. But such a definition is not automatically applicable to a physical situation. In order to be fully effective any definition of a physical quantity must conform to the physical realities; that is, the definition must include everything that behaves in the same manner physically, and it must exclude everything that behaves in a different manner. The general properties of the space component of rotational or vibrational motion are identical with those of extension space, and where both are present, the total space is the sum of the two.

The meaning of the foregoing statement is rather difficult to grasp because of established habits of thought which preclude the kind of a concept that is here being advanced, but consideration of an illustrative example may be of some assistance. Let us assume that a rotating particle of atomic dimensions exists in a specific location in space and time, and then let us ask, What effect does the presence of this particle have on processes that take place in the extension space at this location? According to the views of Democritus and Newton, there is no effect at all, since space is simply a container in which the particle exists, and unless the particle exerts some kind of a force on the participants in the hypothetical process, a possibility which we are excluding from consideration, it is merely something that is also present in the vicinity. Einstein asserts that inasmuch as the particle has mass, it distorts space-time in its vicinity. The Reciprocal System rejects Einstein’s contention and agrees with Newton that the “container” space is not affected by the existence of the contained particle, but this system asserts that if the particle is rotating with a space displacement, as defined in Chapter VI, then the total space involved in the hypothetical process is the sum of the extension space (the space of the container) plus the space displacement of the rotation. If the particle is rotating with a unit displacement, the space aspect of this rotation constitutes one unit of space, and the total space taking part in physical phenomena in this vicinity is increased by one unit.

In order to see what this means, let us now assume that a beam of light passes through an aggregate in which particles of this kind are present. According to the new theory, the additional space will reduce the apparent velocity of the light beam, when this velocity is measured in the usual manner. The true velocity has not changed. The photons of which the radiation is composed have no motion of their own, and consequently they are at all times and all places carried forward at unit velocity—the velocity of light in vacuum—by the progression of space-time. Interposition of the rotating particles cannot change the velocity of anything which is incapable of moving at all with respect to space-time, and the true velocity of the photons must therefore remain at the velocity of space-time itself, one unit of space per unit of time. However, the presence of the additional space of the rotating particles increases the total amount of space to be traversed by the radiation and therefore increases the time required to traverse a given amount of linear extension. This means a lower velocity on the usual basis of measurement, which takes into account only the extension space. Rotating space displacements are included in the structure of most atoms of matter and, accordingly, we find that the velocity of light in a material medium is less than c, the velocity in a vacuum.

Another interesting and important phenomenon that is made possible by the existence of rotating space displacements is the movement of space through matter. The concept of such a movement is, of course, wholly foreign to the traditional ideas as to the nature of space and of matter, but once we recognize space as an aspect of motion it becomes evident that the space aspect of rotational motion has some possibilities that are altogether out of the question so far as extension space is concerned. A rotating space displacement is entirely independent of extension space. It cannot move with respect to that space, since the relation of these two entities is a relation of space to space, which is not motion, but it can move with respect to a time structure, as the relation of the rotational space displacement to this structure is a relation of space to time, which is motion. Detailed studies of the nature and characteristics of the atoms of matter which were reported in previous publications have shown that the net displacement of these material atoms is in time, and matter therefore constitutes the type of a structure in which rotating space units are able to move.

The simplest rotating space unit is one that is formed by direct addition of one-dimensional rotational space displacement to the basic vibrating unit rotational base. As indicated on Chart B. the compound unit of motion thus derived in the theoretical RS universe is identified as an electron. It is not the kind of an electron that is observed as an individual particle in space, however, as the latter is electrically charged, whereas the theoretical particle, in its normal state, is uncharged.

The relation between the electric charge and the experimental electron has been subject to much difference of opinion in scientific circles ever since this particle was originally discovered. One school of thought has held that the charge is the essence of the electron, and that the so-called particle is in reality nothing more than a free electric charge. Modern opinion tends to favor the view that the electron as observed is actually a particle with a charge, but whether or not it is ever possible for the electron to exist in an uncharged state is a matter of controversy. The uncharged or “bare” electron is a feature of many current theoretical speculations, but some physicists take a dim view of it. Dirac, for instance, calls it an “unphysical concept” and suggests that “Probably in the improved physical picture we shall have in the future the bare electron will not exist at all.”⁴

Now that the Reciprocal System makes an “improved physical picture” available, however, the uncharged electron emerges as an important feature of this picture. In the RS universe it is the movement of these uncharged electrons through matter that accounts for the theoretical phenomenon corresponding to the electric current, as well as for the conduction of heat.

It has been recognized ever since the first discovery of electrical phenomena that there are some marked differences in behavior between static electricity and current electricity, and the early investigators were undecided as to whether these were two different phenomena or merely two different manifestations of the same thing. But when it was found that a flow of static charges produced the same magnetic effects as a flow of the current generated by a Voltaic pile, the supporters of the unitary hypothesis gained the upper hand, and since the days of Faraday the electric current has been regarded as a flow of charges or charged particles. Subsequently the hypothetical charged particles were identified as electrons.

However, the general acceptance of this theory that current electricity is simply static electricity in motion has been based on the discovery of points of similarity between the two phenomena, not on any plausible explanation of the observed points of difference. The behavior of static charges in motion is not the same as that of an electric current, and the behavior of a conductor raised to a high electric potential from a source of current is not the same as that of an object with a large static charge. For example, the inductive effects of a potential from a current source are very minor compared to those that would be experienced from an equivalent static charge. Then, again, the static charges repel each other and are therefore located on the surface of the charged object, whereas the direct relation of the conductivity of a conductor to its cross-sectional area indicates that no such effect is present in current electricity. This latter point is, in itself, strong evidence that the particles, which constitute the current, are not charged.

At this juncture it may legitimately be asked why these arguments, none of which is actually new, should carry any more weight now than they have done in the past. The answer is that the question now at issue is altogether different from what it has been previously. Up to this time there has been only one plausible theory available, and the question has been; Is there enough support for this theory to justify accepting it and utilizing it for the time being? Obviously this question had to be answered in the affirmative, as there are many items of evidence that lend credence to the charged particle theory. Probably the most convincing of these, aside from the magnetic effects previously mentioned, is the fact that where a current originates in an electrolytic solution, passes through a conductor, and returns to the solution, the current moving through the solution is undeniably being transferred by charged particles, or charged units of some kind. From this it seems reasonable to assume that a movement of charged particles also exists in the external conductor.

But now we are confronted with a totally different question. A new theory has appeared to challenge the theory of the charged particle, and the question now is; Which of these theories is correct? In this context all of the weaknesses and contradictions that could be overlooked when the charged particle theory had the field all to itself become strong arguments against that theory, since the new theoretical system is in agreement with all of the known facts or, at least, is not inconsistent with any of them. Under the circumstances the charged particle theory is no longer tenable.

In view of the sharp distinction which the new system makes between those phenomena which involve electric charges and those which are due to the presence of uncharged electrons, the subjects that are customarily treated under the general heading of electricity will have to be separated into two groups for present purposes. A discussion of the electrolytic process and other items involving electric charges will be postponed until after the general nature of these charges is explained in the next chapter. At this time we will take a brief look at some of the important features of the electric current as we find it in the theoretical RS universe.

One of the most significant conclusions of this new development is that the electrons move through the atoms of matter, not through the space between the atoms. In this connection, it does not seem to have been recognized that there is a serious weakness in the present-day theory that views the electrons as moving through the interstices between the atoms, since this does not explain why the current is confined within the conductor. If the electrons can move readily through the spaces between the atoms, then there is no visible reason why they should not move through the spaces between the outside atoms of the conductor and thus escape out into the surrounding space. An attempt has been made to explain this situation by means of another demon (that is, an ad hoc force invented for this specific purpose). It has been postulated that a “potential barrier” at the surface of the conductor prevents escape of the electrons, and the existence of surface forces which keep the atoms of a liquid confined within the aggregate until they acquire a certain minimum amount of kinetic energy is often cited as an analogy which supports this hypothesis. Shortley and Williams, for example, give us this explanation:

Electrons within a metal can be regarded as “free” so far as electric current within the metal is concerned, but they are confronted by a “barrier” at the surface of the metal. In order to escape from the metal, an electron must have sufficient energy to pass through the surface barrier. The minimum energy an electron must have in order to escape may be called the “height of the potential barrier” at the metal surface…. The escape of electrons from a metal is quite analogous to the escape of the molecules of a liquid in evaporation, where there are also barrier forces tending to prevent the escape.¹¹¹

The flaw in this analogy is that there is a known force which accounts for the “barrier” to evaporation—the cohesion between the molecules of the liquid, which is effective not only at the surface but throughout the liquid aggregate, as can easily be demonstrated by suspending a liquid drop from a solid surface—but there is no known force of cohesion between the electrons. Indeed, they should repel each other if they are charged, and in that event the “potential barrier” comparable to that which exists in the liquid should be negative. Neither is there any evidence of a force of cohesion between the electrons and the atoms of matter, nor could there be any such force without offering the same resistance to passage of the electrons through the conductor as out of the conductor.

This explanation thus turns out to be one of those false analogies that are based on casual and superficial consideration of the phenomena in question without any adequate effort to examine the validity of the assumption that they are of a similar nature. The “barrier” to the escape of a liquid molecule by evaporation is a genuine restraining force whose existence can be demonstrated independently of the evaporation phenomenon and whose magnitude can be measured. The “barrier” to the escape of an electron from a conductor is purely hypothetical; it cannot be a restraining force of the same nature as that which holds the liquid molecule back, and there is no reasonable suggestion as to any other way in which such a barrier might originate.

In the theoretical RS universe there actually is a barrier preventing escape of the uncharged electrons, but it is not merely a hurdle comparable to the force that resists evaporation; it is a positive barrier. An uncharged electron can move freely through the atoms of a conductor, but it cannot move at all through space, either inside or outside the conductor. Space (electrons) cannot move through space (extension) simply because the relation of space to space is not motion. But the uncharged electron can move through matter, because the net displacement of the material atom is in time, and the relation of space to time is motion.

What actually happens at the surface of the conductor is that if enough additional energy is imparted to the electron by any one of a number of possible mechanisms—thermal excitation, electrical potentials, high energy photons, etc.—the electron acquires a charge, and in the charged condition it is able to move through either time or space, for reasons which will be explained in the next chapter. The energy required to expel the electron from the conductor is not used in penetrating a barrier but in creating the electric charge and in giving the charged electron sufficient kinetic energy to overcome the gas pressure in the ambient space. Evacuating the air can reduce this pressure, and most devices designed for the production of charged electrons therefore operate in a partial vacuum.

The general effects of motion of space (electrons) through matter are identical with the effects of motion of matter through space (extension). One of the most obvious results of the current flow is an increase in the temperature of the conductor. This is commonly attributed to frictional effects as the electrons make their way through the inter-atomic space, but since the electron moves through matter, not through the open spaces, such an explanation cannot apply in the RS universe. Here we find that passage of electrons (units of space) through a conductor is equivalent to a movement of the atoms of the conductor through the same amount of extension space. The motion of space (electrons) through matter thus adds to the previously existing thermal velocity of the atoms—movement of matter through space (extension)—and since it is the total velocity that determines the temperature, one effect of the electron flow is to raise the temperature of the conductor.

The rate of transfer of energy from the electric current to the thermal motion of the atoms of the conductor is the factor which determines the amount of current flow that will take place in response to a given potential difference. It is expressed as resistance, the ratio of potential to current. As can be seen from the explanation in the preceding paragraph, a conductor has no resistance at all unless thermal motion is present. The electrons (units of space) can move through motionless matter freely without expenditure of energy, just as matter can move freely through open space. If thermal motion is present they increase the magnitude of that motion, but if there is no such motion to begin with the increase in space due to the current flow has no thermal effect. The resistance of a pure conductor is therefore zero at zero absolute temperature and it increases linearly with increase in temperature.

Although all material substances are basically time structures—that is, their net displacement is in time—they are not all equally good conductors of electricity, as most substances contain some space displacement, for reasons that will be explained in Chapter XVI, and where a substantial amount of space is involved the electrons either cannot pass through such substances at all or can do so only with a certain amount of difficulty (expenditure of energy). The various forms of matter therefore range all the way from very good conductors to substances, which are almost as effective insulators as space itself. Presence of small amounts of non-conducting materials in conductors often has a disproportionately large effect on the resistance, particularly at low temperatures, and the behavior of conductors containing impurities often deviates considerably from the theoretical pattern of the pure conductor. For instance, most conductors approach a finite value, the so-called “residual resistance” as they approach zero temperature rather than decreasing all the way to zero.

The rate of flow of the electric current, commonly designated by the symbol I, is expressed in terms which are equivalent to the number of electrons per unit of time. Inasmuch as each electron is a unit of space, what we have here is units of space per unit of time. This is the definition of velocity, hence the flow of current is a velocity. Since the kinetic energy of matter moving through extension space is proportional to the square of the velocity, it follows that the thermal energy of an electric current (the heat developed by the current flow) is proportional to I². This conclusion is confirmed by experiment.

Electromotive force, or potential, is analogous, in its general aspects, to gas pressure, which is force per unit area. The magnitude of the potential at any point may be increased in the same manner that gas pressure is increased, either by introducing more electrons with the same average velocity or by imparting a greater velocity to the electrons already present. If we connect one end of a metallic wire to a battery or other source of electrons, the electrons which enter the wire from this source raise the potential at the point of entrance and cause a flow of current (electrons) until equilibrium is reestablished. Similarly, if one end of the wire is heated, the additional thermal velocity of the electrons raises the electric potential and causes a flow of current toward the other end of the wire. The immediate effect in this case is equilibrium between a lower concentration of high velocity electrons at one end of the wire and a higher concentration of low velocity electrons at the other end. Ultimately both the velocities and the concentrations will equalize if the wire is thermally isolated. In the usual situation, however, there is a thermal interchange between the wire and its environment. The high velocity electrons arriving at the cold end of the wire transfer part of their energy to the atoms of the wire in order to reach a thermal equilibrium, but the atoms continually destroy the equilibrium by losing heat to their environment. This means that the heat flow, or conduction of heat from one end of the wire to the other, unlike the flow of current from the battery, will continue as long as the ambient temperature at one end is greater than that at the other.

It has long been recognized that the movement of electrons in this manner is a very logical explanation of the metallic conduction of heat, but the obstacle that has prevented unqualified acceptance of this idea is the absence of any indication of the increase in specific heat which would seem to be required by the electron movement. The answer to this objection is now provided by the Reciprocal System. The thermal motion of the electrons, this new system says, is not an addition to the thermal motion of the atoms, as previous theory has assumed; it is an integral part of the total atomic motion. A mass m attains a certain temperature T when the thermal velocity of its constituent atoms reaches a specific average value n. From this standpoint it is immaterial whether the velocity consists entirely of motion of the atoms through space (extension) or partly of such motion and partly of motion of space (electrons) through the mass. The total velocity v corresponding to the temperature T is the same in either case, hence the conduction of heat by movement of electrons has no effect on the specific heat.

Since the thermal characteristics of different kinds of matter vary considerably, it follows that the nature of the equilibrium between the motion of the electrons and the motion of the atoms of matter is also subject to substantial variations. In the absence of any externally generated electric potential the relative potential of the electrons therefore depends on the characteristics of the conductor. In general a low resistance conductor such as copper will have a lower electrical potential than a conductor with a higher resistance. If we place two such conductors in contact we therefore generate what is known as a contact potential. A flow of electrons will take place from zinc to copper, for example, until the density of the electrons in the copper becomes high enough to offset the greater velocity of the electrons in the zinc. The same differences between the equilibrium potentials in different materials are responsible for a number of other phenomena, such as the thermoelectric effect, the Peltier effect, the Thomson effect, etc., which are beyond the scope of this work but have been discussed in previous publications.

A hundred years ago one of the questions that loomed large in the thinking of scientists and laymen alike was: What is electricity? Today this question is seldom asked by laymen and almost never by scientists, not because it has been satisfactorily answered, but because scientists have been able to persuade both themselves and the general public that there is no answer; that electricity simply has to be accepted without explanation as something that exists. The Reciprocal System has now retrieved this question from the limbo into which it was cast, and has provided the allegedly non-existent answer: number ten in our list of Outstanding Achievements. This answer, the concept of space moving through matter, will no doubt be hard for many persons to accept, but this is only because the new concept of space itself seems so strange. Homo sapiens has not thought about space in this way, or looked at space in this way, before, and he distrusts the unfamiliar.

All that is necessary here is to recognize that space is an aspect of motion, and that extension space, the only space that has been recognized heretofore, is only one of the ways in which space may manifest itself. The space aspect of rotational motion is obviously something other than linear extension, and as soon as it is realized that this is actually space, in the same sense that extension space is space, the shock that usually accompanies the first encounter with such a seemingly bizarre concept as that of space moving through matter will wear off.